Washington Rep. Cathy McMorris Rodgers looks set to win the race for House Republican Conference chairman, which she will contest against Georgia Rep. Tom Price in a few weeks.

The conference chair represents the No. 4 House GOP leadership position, behind the speaker, majority leader, and whip. So McMorris Rodgers would become the most powerful woman in the GOP.

A woman hasn’t occupied a top Republican leadership position in the last five years. If McMorris loses, the party risks having no women in a power slot.

Many House heavyweights are lining up behind her, Politico reports. That includes seven top committee chairmen, many of whom are lobbying their colleagues on McMorris Rodgers’ behalf. Members close to House Speaker John Boehner are backing her too.

McMorris Rodgers’s supporters say victory is in the bag, but that’s hard to verify given that the vote will be a secret ballot.

She wants the party to make a wider embrace. “I think there’s some way that we can take our message to every corner of the country,” McMorris Rodgers told Politico.

“We have a record number of women serving in our conference, we have African-Americans, we have Hispanics. We’re younger than the Democrats. Our leadership team on average is 20 years younger than their leadership team. We need to tell our story a little bit more and put forth the face of the Republican Party that is reflective of Americans all across this country.”